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%I #5 May 15 2014 10:17:38
%S 6,9,13,14,18,19,25,27,28,39,40,41,44,46,49,57,67,78,82,87,90,92,93,
%T 99,100,103,109,114,115,123,125,130,132,133,135,140,150,151,160,165,
%U 169,173,182,188,193,204,208,209,211,214,217,224,230,237,238,240,244
%N Positive integers k for which k^3 is greedy-summable.
%C Greedy summability is defined at A242293.
%H Clark Kimberling, <a href="/A242295/b242295.txt">Table of n, a(n) for n = 1..400</a>
%e Let s(n) = n^3 = A000578(n). Then
%e a(1) = 6; s(6) = 216 = 125 + 64 + 27;
%e a(2) = 9; s(9) = 729 = 512 + 216 + 1;
%e a(3) = 13; s(13) = 2197 = 1728 + 343 + 125 + 1;
%e a(4) = 14; s(14) = 2744 = 2197 + 512 + 27 + 8.
%t z = 200; s = Table[n^3, {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]
%t r[n_] := s[[n]] - Total[t[[n]][[2]]];
%t tr = Table[r[n], {n, 2, z}] (* A242293 *)
%t c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242294 *)
%t f = 1 + Flatten[Position[tr, 0]] (* A242295 *)
%t f^3 (* A242296 *) (* _Peter J. C. Moses_, May 06 2014 *)
%Y Cf. A242293, A242294, A242296, A241833, A242284, A000578.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 10 2014
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